Variable Sample Size Control Chart Research Articles

Optimal designs of variable sample size control chart for monitoring the multivariate coefficient of variation in short production runs

Short production runs are common in industries that require high flexibility and variety in manufacturing. Only a limited amount of researches on multivariate control charts in short production runs exists in the literature. This article proposes two one-sided adaptive charts for monitoring the multivariate coefficient of variation (MCV) in short production runs by varying the sample size (called the VSS MCV SPR charts). The two one-sided adaptive charts are the upper-sided and lower-sided VSS MCV SPR charts for monitoring increasing and decreasing shifts, respectively, in the process MCV. The optimal parameters of the VSS MCV SPR charts in minimizing the out-of-control truncated average run length (TARL) value, for various shift sizes, are presented. The proposed VSS MCV SPR charts outperform their non-adaptive short production runs Shewhart MCV counterparts (called the SH MCV SPR charts), as the former have smaller out-of-control TARL value than the latter, for the same shift size. The sensitivity of the VSS MCV SPR charts, in terms of the probability of signaling an alarm within I inspections is also studied, where the VSS MCV SPR charts surpass their corresponding SH MCV SPR charts. An example for implementing the VSS MCV SPR charts is provided.

Variable sample size control chart for monitoring process capability index <i>C<SUB align="right">pm</i>

Process capability indices (PCIs) provide numerical measures of process reproduction capability and are effective tools for quality assurance. In the present paper, we develop a variable sample size control chart, namely VSSCpm, to monitor PCIs for industry manufacturing to improve product quality. We setup the control limits; determine the upper and lower warning limits, fixed sample size, central region sample size, and warning region sample size for the control chart; and apply them to monitor PCI Cpm. We also use the average run length (ARL) as a monitoring performance indicator. To increase the in-plant applicability of the proposed method, we tabulate the performance value of the ARL for various commonly used situations. We perform a sensitivity analysis to study the effects of model parameters on the monitoring performance and then present an example to illustrate the proposed procedure.

Monitoring the coefficient of variation using a variable sample size control chart in short production runs

Monitoring the coefficient of variation (CV) is an effective approach to monitor a process when both the process mean and the standard deviation are not constant but, nevertheless, proportional. Until now, few contributions have investigated the monitoring of the CV for short production runs. This paper proposes an adaptive Shewhart control chart implementing a variable sample size (VSS) strategy in order to monitor the coefficient of variation in a short production run context. Formulas for the truncated average run length are derived. Moreover, a comparison is performed with a Fixed Sampling Rate Shewhart chart for the CV in order to evaluate the performance of each chart in a short run context. An example illustrates the use of this chart on real data.

Monitoring the coefficient of variation using a variable sample size control chart

This paper proposes an adaptive Shewhart control chart implementing a variable sample size strategy in order to monitor the coefficient of variation. The goals of this paper are as follows: (a) to propose an easy-to-use 3-parameter logarithmic transformation for the coefficient of variation in order to handle the variable sample size aspect; (b) to derive the formulas for computing the average run length, the standard deviation run length, and the average sample size and to evaluate the performance of the proposed chart based on these criteria; (c) to present ready-to-use tables with optimal chart parameters minimizing the out-of-control average run length as well as the out-of-control average sample size; and (d) to compare this chart with the fixed sampling rate, variable sampling interval, and synthetic control charts. An example illustrates the use of the variable sample size control chart on real data gathered from a casting process.